||Computer-aided Explorations of Modular Spaces of Real Polynomials: Giving Geometric Life to Routine Algebra
||Gabriel KATZ and Vladimir NODELMAN
We suggest a novel visual approach to teaching topics in elementary algebra from a viewpoint that is characteristic of modern mathematics. It puts emphasis on families of mathematical like-objects, rather than on a prototypical object from a given family. Thanks to rich computer-supported virtual mathematical environments (like VisuMatica), it becomes feasible to convey this advanced circle of ideas to students with a modest mathematical background. In the paper, we us illustrate our approach with a few basic examples; they revolve around the problem of solving quadratic and cubic equations.